Nuprl Lemma : pcw-pp-barred_wf

[P:Type]. ∀[A:P ⟶ Type]. ∀[B:p:P ⟶ A[p] ⟶ Type]. ∀[C:p:P ⟶ a:A[p] ⟶ B[p;a] ⟶ P]. ∀[pp:PartialPath].
  (Barred(pp) ∈ ℙ)


Proof




Definitions occuring in Statement :  pcw-pp-barred: Barred(pp) pcw-pp: PartialPath uall: [x:A]. B[x] prop: so_apply: x[s1;s2;s3] so_apply: x[s1;s2] so_apply: x[s] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T pcw-pp: PartialPath so_lambda: λ2x.t[x] so_apply: x[s] so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3]
Lemmas referenced :  pcw-pp-barred_wf0 pcw-pp_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution setElimination thin rename lemma_by_obid isectElimination hypothesisEquality sqequalRule lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache functionEquality cumulativity universeEquality

Latex:
\mforall{}[P:Type].  \mforall{}[A:P  {}\mrightarrow{}  Type].  \mforall{}[B:p:P  {}\mrightarrow{}  A[p]  {}\mrightarrow{}  Type].  \mforall{}[C:p:P  {}\mrightarrow{}  a:A[p]  {}\mrightarrow{}  B[p;a]  {}\mrightarrow{}  P].
\mforall{}[pp:PartialPath].
    (Barred(pp)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_14-AM-06_13_12
Last ObjectModification: 2015_12_26-PM-00_05_41

Theory : co-recursion


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